document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=272272>Question 272272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having extreme difficulty with this section of my homework.  I have to find a polynomial function of least degree having only real coefficients with zeros.<BR>\n" );
document.write( "The book tells me that f(x)=x-(1+i) has 1+i as a zero, but the conjugate 1-i is not a zero.  Why?  If I use the synthetic division (as the book says) to figure out if f(k)=0, I get don't understand why 1-i is not a zero.  All I keep getting is the same equation by using synthetic division.\r<BR>\n" );
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document.write( "The problem I am having to do it:\r<BR>\n" );
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document.write( "2+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+3+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, 2-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+3+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and 2+3i.\r<BR>\n" );
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document.write( "By not understanding why why 1-i is not a zero, I am confused as to what is a zero in the above equation.\r<BR>\n" );
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document.write( "I THINK that 2+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+3+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 2+3i are going to be zeros for the problem, giving me an equation that looks something like:\r<BR>\n" );
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document.write( "f(x)= [x-(2+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+3+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >)][x-(2-<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28+3+%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28+3+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >)][x-(2+3i)][x-(2-3i)]\r<BR>\n" );
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document.write( "If someone could please help me with this I would GREATLY appreciate it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #199234 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=199234\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x-(1+i)=0<BR>\n" );
document.write( "let 1+i=a so you will understand better<BR>\n" );
document.write( "x-a=0<BR>\n" );
document.write( "x=a<BR>\n" );
document.write( "x=1+i piece of cake. you are over-thinking this one.<BR>\n" );
document.write( "A first degree equation has only one zero.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );